Math 55 Worksheet July 28, 2011 Adapted from worksheets by Rob Bayer, Summer 2009. Warmups 1. If you roll 3 fair dice, what is the expected value of the sum of the dice? Problems Proper 1. What is the probability of getting exactly 3 heads when ﬂipping a coin 5 times if the coin is twice as likely to come up heads as tails? 2. Suppose you have 3 fair dice and 1 loaded die that comes up 6 with probability 1 3 and each other value with probability 2 15 . If you pick a die from this set at random, roll it twice, and get a 6 twice, what’s the probability that you picked the loaded die? 3. A test for the Common Banana Virus is 98% speciﬁc (that is, 98% of the time the test will be negative for someone without the disease, and the remaining 2% of the time it will give a false positive) and 99% sensitive (ie, 99% of the time the test will be positive for someone who has the disease, and 1% of the time the test gives a false negative). Just 1% of the population carries CBV. (a) If you test positve, what’s the probability that you actually have CBV?

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